Wednesday, June 3, 2015

Semester 2 Review and Next Year Preview (Day 180)

This is the final week of school for the geometry student I tutor. He is an eighth grader completing his middle school years, so he had promotion ceremonies this week, not finals. Therefore the only student I'm tutoring this week is a high school student preparing for his Algebra II final. I'll tutor him tomorrow night since his final is on Friday.

So he didn't finish the last four chapters of the Glencoe text, and these are some big chapters. Chapter 10 is on circles -- and most of the circle questions on the PARCC test, while spread out among several U of Chicago chapters (8, 11, 13, 15) are concentrated in this single Glencoe chapter. (That's right -- not only did we not reach the pi lesson by Pi Day, but we don't reach it at all.) Chapters 11 and 12 are on area and volume. The final chapter of the Glencoe text is on probability -- the presence of this chapter in a Geometry text may be influenced by California State Standards, which state that probability be included with Geometry.

My student began Algebra I in the seventh grade, but didn't finish the text. So his teacher completed Algebra I during the first quarter, then moved on to Geometry the last three quarters. Thus, in a way, he took an integrated class this year. I wonder whether he'll finish the last four chapters of Geometry as a freshman before moving on to Algebra II.

But that's enough about my student. Let's get to my own plans for next year. I've spent several posts over the past couple of months discussing what changes I'd make to my lesson plan -- and these changes were mostly due to either the content or the timing of the Common Core tests.

Let's recall that I work for two different districts. One of these had an Early Start calendar, and I based my blog calendar on that district. But I have decided to switch the blog calendar to one based on my other district.

Last year, this district started school after Labor Day. But this year, the district decided to start school before the holiday, on August 26th. Notice that this is not nearly early enough in August to have the first semester end by Christmas.

I've noticed that there are many schools that start in late August -- before Labor Day, yet still extend the first semester into January. I've heard that my district wanted to convert to a full Early Start calendar, but the union opposed it, and so August 26th was a compromise. This is about a week earlier than last year, while Labor Day itself is nearly a week later (September 7th rather than the 1st), so school is now starting two weeks earlier than it would under a Labor Day start.

I believe that much of the phenomenon of Christmas creep -- the trend of retailers beginning the holiday sales earlier each year -- goes back to the structure of the Gregorian calendar and the fact that 365 isn't evenly divisible by seven. Traditionally, the holiday shopping season began on Black Friday, the day after Thanksgiving. Each year, Turkey Day is a day or so earlier than the previous year, so this would automatically extend the shopping season an extra day each year. But then Thanksgiving would reach its earliest date of November 22nd, when it would jump back to November 28th. Of course retailers don't want to shorten the shopping season, so instead they would begin the holiday sales a week before Thanksgiving. Each year as the November holiday works its way from the 28th up to the 22nd, the sales would begin a week before Thanksgiving, until the next jump back to the 28th, at which point sales begin two weeks before the holiday, and so on.

Now the idea of First Day of School creep isn't exactly like Christmas creep. After all, the purpose of Christmas creep is to extend the holiday shopping season. But the length of the public school year remains at 180 days no matter what. Sometimes the earlier start of the year means that the school year ends earlier as well, and other times it means that the holiday breaks are longer.

Indeed, the recent trend is to extend Thanksgiving break to an entire week. I know that some local districts state that they are starting a week before Labor Day in order to have the longer fall break -- the second semester would still start and end at the same time as it did before the change. But I know of another school district that started a week before Labor Day for this reason -- and then five years later, it was starting two weeks before the end-of-summer holiday.

And of course, I can't help but notice that these districts are changing the calendar in exactly the year that Labor Day jumps back from September 1st to the 7th. Indeed, I can see how a district can move gradually to a full Early Start calendar without fear of union disapproval -- simply start school a day or so earlier each year. It will remain a fixed number of weeks before Labor Day until the holiday jumps back from the 1st to the 7th, when the start of school gains another week on Labor Day.

For now, I'll refer to schools in districts such as mine as Middle Start schools. Middle Start schools typically begin about two or three weeks before Labor Day. The second semester begins either Martin Luther King Jr. Day or the week after -- not around the 1st of February as in Labor Day start schools, nor right after winter break as in Early Start schools.

I've already posted what my ideal Geometry class would look like. I set it up so that it could fit either an Early Start or a Labor Day start calendar, but not necessarily a Middle Start calendar. The big problem is that I wanted to avoid having units jump over holidays -- especially the major breaks like Thanksgiving and winter break. My ideal schedule fit the holidays for the other two calendars but would jump over holiday breaks on the Middle Start calendar. To me, it's more important to avoid having students forget what they learned over the long breaks than it is to keep the U of Chicago chapters intact -- especially since I'm changing the order of the U of Chicago lessons anyway.

So instead of having each unit end right where a U of Chicago chapter ends, my units will end about midway through the chapter -- approximately the fourth section of each lesson. By doing so, my first semester will end up looking like this:

Unit 1: Geometry Basics, 2 weeks (Chapter 1 in U of Chicago)
Unit 2: Reflections, 5 weeks (up to Section 4-4)
Unit 3: Rotations, 3 weeks (up to Section 5-4)
Unit 4: Translations, 3 weeks (up to Section 6-4)
Unit 5: Glide Reflections, 3 weeks (up to Section 7-4)
Review and Final: 3 weeks (Sections 7-5 through 7-7)

Originally, I wrote that my units will be closer to a month than three weeks in length. As it turns out, three-week units happened to fit my calendar better, especially in the second quarter. There are three weeks from the start of the quarter to Thanksgiving break, then three weeks from Thanksgiving to winter break, and then three weeks from winter break to the end of the semester. Notice that even my opening unit fits the holidays, as my Chapter 1 unit posted on the blog last year can remain intact and fit before the Labor Day holiday/

The second semester is trickier because I don't know when the Common Core tests will begin. On an Early Start calendar, the SBAC is before the AP, and on a Labor Day Start calendar, the SBAC is after the AP. This would place the SBAC on a Middle Start calendar right on top of the AP -- which is undesirable since some juniors have to take both SBAC and AP exams.

Since I'm not sure when the SBAC will be, the second semester is tentative:

Unit 6: Dilations, 3 weeks (Chapter 12)
Unit 7: Coordinate Geometry, 3 weeks (Chapter 11)
Unit 8: Area and Volume, 3 weeks (Chapters 8 and 10, includes Pi Day)
Unit 9: Trigonometry, depends on SBAC (Chapter 14)
Unit 10: Circles, depends on SBAC (various U of Chicago chapters)

Ideally, I'd like to extend area and volume to a month each, as these are important chapters. But by this point we're approaching spring break, and the last thing I want to do is force students to remember the formulas over the holidays (which is what ended up happening last year). Dilations and coordinate geometry could be pushed back to five weeks total -- last year they spanned four weeks on the blog, but I want to add transformations to the coordinate geometry section. Circles must be the final unit before the Common Core tests no matter what.

Finally, all of this assumes that my employment situation doesn't change. If I end up working in another school next year, then naturally my schedule will follow the calendar for that school.

And so this concludes my first year of teaching Common Core Geometry on this blog. Of course, I will write a few posts over the summer break before beginning my second year on August 26th. I want to focus on two topics during the summer:

-- What I like, and what I'd change, about Common Core Math
-- Spherical Geometry

I've briefly discussed how I would change Common Core Math during previous holiday breaks, and so I want to use the summer to discuss this in more detail. As for spherical geometry, I want to look back at that old Legendre text, since it contains some information about spherical geometry.

I like posting after I have tutoring sessions. So I'll post my first summer blog entry on Friday. After tutoring an Algebra II student, it will be a great time to post about Common Core Math, and specifically the tests that students have to take as juniors after taking Algebra II.

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